### Abstract

This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this paper, we present the first algorithm that computes the geodesic diameter of a given polygonal domain in worst-case time O(n ^{7.73}) or O(n ^{7} (logn + h)). Among other results, we show the following geometric observation: the geodesic diameter can be determined by two points in its interior. In such a case, there are at least five shortest paths between the points.

Original language | English |
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Title of host publication | Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings |

Pages | 500-511 |

Number of pages | 12 |

Edition | PART 1 |

DOIs | |

Publication status | Published - 2010 |

Event | 18th Annual European Symposium on Algorithms, ESA 2010 - Liverpool, United Kingdom Duration: 2010 Sep 6 → 2010 Sep 8 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 6346 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th Annual European Symposium on Algorithms, ESA 2010 |
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Country | United Kingdom |

City | Liverpool |

Period | 10/9/6 → 10/9/8 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings*(PART 1 ed., pp. 500-511). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6346 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-15775-2_43